## Communications in Mathematical Sciences

### Vanishing viscosity and the accumulation of vorticity on the boundary

J. P. Kelliher

#### Abstract

We say that the vanishing viscosity limit holds in the classical sense if the velocity for a solution to the Navier-Stokes equations converges in the energy norm uniformly in time to the velocity for a solution to the Euler equations. We prove, for a bounded domain in dimension 2 or higher, that the vanishing viscosity limit holds in the classical sense if and only if a vortex sheet forms on the boundary.

#### Article information

Source
Commun. Math. Sci., Volume 6, Number 4 (2008), 869-880.

Dates
First available in Project Euclid: 18 December 2008